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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.geometry.euclidean.threed;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.awt.geom.AffineTransform;<a name="line.19"></a>
<FONT color="green">020</FONT>    import java.util.Collection;<a name="line.20"></a>
<FONT color="green">021</FONT>    <a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.geometry.Vector;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.geometry.euclidean.oned.Euclidean1D;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.geometry.euclidean.twod.Euclidean2D;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.geometry.euclidean.twod.SubLine;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.geometry.euclidean.twod.Vector2D;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.geometry.partitioning.AbstractRegion;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.geometry.partitioning.BSPTree;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.geometry.partitioning.BSPTreeVisitor;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.geometry.partitioning.BoundaryAttribute;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math3.geometry.partitioning.Hyperplane;<a name="line.31"></a>
<FONT color="green">032</FONT>    import org.apache.commons.math3.geometry.partitioning.Region;<a name="line.32"></a>
<FONT color="green">033</FONT>    import org.apache.commons.math3.geometry.partitioning.RegionFactory;<a name="line.33"></a>
<FONT color="green">034</FONT>    import org.apache.commons.math3.geometry.partitioning.SubHyperplane;<a name="line.34"></a>
<FONT color="green">035</FONT>    import org.apache.commons.math3.geometry.partitioning.Transform;<a name="line.35"></a>
<FONT color="green">036</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.36"></a>
<FONT color="green">037</FONT>    <a name="line.37"></a>
<FONT color="green">038</FONT>    /** This class represents a 3D region: a set of polyhedrons.<a name="line.38"></a>
<FONT color="green">039</FONT>     * @version $Id: PolyhedronsSet.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.39"></a>
<FONT color="green">040</FONT>     * @since 3.0<a name="line.40"></a>
<FONT color="green">041</FONT>     */<a name="line.41"></a>
<FONT color="green">042</FONT>    public class PolyhedronsSet extends AbstractRegion&lt;Euclidean3D, Euclidean2D&gt; {<a name="line.42"></a>
<FONT color="green">043</FONT>    <a name="line.43"></a>
<FONT color="green">044</FONT>        /** Build a polyhedrons set representing the whole real line.<a name="line.44"></a>
<FONT color="green">045</FONT>         */<a name="line.45"></a>
<FONT color="green">046</FONT>        public PolyhedronsSet() {<a name="line.46"></a>
<FONT color="green">047</FONT>            super();<a name="line.47"></a>
<FONT color="green">048</FONT>        }<a name="line.48"></a>
<FONT color="green">049</FONT>    <a name="line.49"></a>
<FONT color="green">050</FONT>        /** Build a polyhedrons set from a BSP tree.<a name="line.50"></a>
<FONT color="green">051</FONT>         * &lt;p&gt;The leaf nodes of the BSP tree &lt;em&gt;must&lt;/em&gt; have a<a name="line.51"></a>
<FONT color="green">052</FONT>         * {@code Boolean} attribute representing the inside status of<a name="line.52"></a>
<FONT color="green">053</FONT>         * the corresponding cell (true for inside cells, false for outside<a name="line.53"></a>
<FONT color="green">054</FONT>         * cells). In order to avoid building too many small objects, it is<a name="line.54"></a>
<FONT color="green">055</FONT>         * recommended to use the predefined constants<a name="line.55"></a>
<FONT color="green">056</FONT>         * {@code Boolean.TRUE} and {@code Boolean.FALSE}&lt;/p&gt;<a name="line.56"></a>
<FONT color="green">057</FONT>         * @param tree inside/outside BSP tree representing the region<a name="line.57"></a>
<FONT color="green">058</FONT>         */<a name="line.58"></a>
<FONT color="green">059</FONT>        public PolyhedronsSet(final BSPTree&lt;Euclidean3D&gt; tree) {<a name="line.59"></a>
<FONT color="green">060</FONT>            super(tree);<a name="line.60"></a>
<FONT color="green">061</FONT>        }<a name="line.61"></a>
<FONT color="green">062</FONT>    <a name="line.62"></a>
<FONT color="green">063</FONT>        /** Build a polyhedrons set from a Boundary REPresentation (B-rep).<a name="line.63"></a>
<FONT color="green">064</FONT>         * &lt;p&gt;The boundary is provided as a collection of {@link<a name="line.64"></a>
<FONT color="green">065</FONT>         * SubHyperplane sub-hyperplanes}. Each sub-hyperplane has the<a name="line.65"></a>
<FONT color="green">066</FONT>         * interior part of the region on its minus side and the exterior on<a name="line.66"></a>
<FONT color="green">067</FONT>         * its plus side.&lt;/p&gt;<a name="line.67"></a>
<FONT color="green">068</FONT>         * &lt;p&gt;The boundary elements can be in any order, and can form<a name="line.68"></a>
<FONT color="green">069</FONT>         * several non-connected sets (like for example polyhedrons with holes<a name="line.69"></a>
<FONT color="green">070</FONT>         * or a set of disjoint polyhedrons considered as a whole). In<a name="line.70"></a>
<FONT color="green">071</FONT>         * fact, the elements do not even need to be connected together<a name="line.71"></a>
<FONT color="green">072</FONT>         * (their topological connections are not used here). However, if the<a name="line.72"></a>
<FONT color="green">073</FONT>         * boundary does not really separate an inside open from an outside<a name="line.73"></a>
<FONT color="green">074</FONT>         * open (open having here its topological meaning), then subsequent<a name="line.74"></a>
<FONT color="green">075</FONT>         * calls to the {@link Region#checkPoint(Vector) checkPoint} method will<a name="line.75"></a>
<FONT color="green">076</FONT>         * not be meaningful anymore.&lt;/p&gt;<a name="line.76"></a>
<FONT color="green">077</FONT>         * &lt;p&gt;If the boundary is empty, the region will represent the whole<a name="line.77"></a>
<FONT color="green">078</FONT>         * space.&lt;/p&gt;<a name="line.78"></a>
<FONT color="green">079</FONT>         * @param boundary collection of boundary elements, as a<a name="line.79"></a>
<FONT color="green">080</FONT>         * collection of {@link SubHyperplane SubHyperplane} objects<a name="line.80"></a>
<FONT color="green">081</FONT>         */<a name="line.81"></a>
<FONT color="green">082</FONT>        public PolyhedronsSet(final Collection&lt;SubHyperplane&lt;Euclidean3D&gt;&gt; boundary) {<a name="line.82"></a>
<FONT color="green">083</FONT>            super(boundary);<a name="line.83"></a>
<FONT color="green">084</FONT>        }<a name="line.84"></a>
<FONT color="green">085</FONT>    <a name="line.85"></a>
<FONT color="green">086</FONT>        /** Build a parallellepipedic box.<a name="line.86"></a>
<FONT color="green">087</FONT>         * @param xMin low bound along the x direction<a name="line.87"></a>
<FONT color="green">088</FONT>         * @param xMax high bound along the x direction<a name="line.88"></a>
<FONT color="green">089</FONT>         * @param yMin low bound along the y direction<a name="line.89"></a>
<FONT color="green">090</FONT>         * @param yMax high bound along the y direction<a name="line.90"></a>
<FONT color="green">091</FONT>         * @param zMin low bound along the z direction<a name="line.91"></a>
<FONT color="green">092</FONT>         * @param zMax high bound along the z direction<a name="line.92"></a>
<FONT color="green">093</FONT>         */<a name="line.93"></a>
<FONT color="green">094</FONT>        public PolyhedronsSet(final double xMin, final double xMax,<a name="line.94"></a>
<FONT color="green">095</FONT>                              final double yMin, final double yMax,<a name="line.95"></a>
<FONT color="green">096</FONT>                              final double zMin, final double zMax) {<a name="line.96"></a>
<FONT color="green">097</FONT>            super(buildBoundary(xMin, xMax, yMin, yMax, zMin, zMax));<a name="line.97"></a>
<FONT color="green">098</FONT>        }<a name="line.98"></a>
<FONT color="green">099</FONT>    <a name="line.99"></a>
<FONT color="green">100</FONT>        /** Build a parallellepipedic box boundary.<a name="line.100"></a>
<FONT color="green">101</FONT>         * @param xMin low bound along the x direction<a name="line.101"></a>
<FONT color="green">102</FONT>         * @param xMax high bound along the x direction<a name="line.102"></a>
<FONT color="green">103</FONT>         * @param yMin low bound along the y direction<a name="line.103"></a>
<FONT color="green">104</FONT>         * @param yMax high bound along the y direction<a name="line.104"></a>
<FONT color="green">105</FONT>         * @param zMin low bound along the z direction<a name="line.105"></a>
<FONT color="green">106</FONT>         * @param zMax high bound along the z direction<a name="line.106"></a>
<FONT color="green">107</FONT>         * @return boundary tree<a name="line.107"></a>
<FONT color="green">108</FONT>         */<a name="line.108"></a>
<FONT color="green">109</FONT>        private static BSPTree&lt;Euclidean3D&gt; buildBoundary(final double xMin, final double xMax,<a name="line.109"></a>
<FONT color="green">110</FONT>                                                          final double yMin, final double yMax,<a name="line.110"></a>
<FONT color="green">111</FONT>                                                          final double zMin, final double zMax) {<a name="line.111"></a>
<FONT color="green">112</FONT>            final Plane pxMin = new Plane(new Vector3D(xMin, 0,    0),   Vector3D.MINUS_I);<a name="line.112"></a>
<FONT color="green">113</FONT>            final Plane pxMax = new Plane(new Vector3D(xMax, 0,    0),   Vector3D.PLUS_I);<a name="line.113"></a>
<FONT color="green">114</FONT>            final Plane pyMin = new Plane(new Vector3D(0,    yMin, 0),   Vector3D.MINUS_J);<a name="line.114"></a>
<FONT color="green">115</FONT>            final Plane pyMax = new Plane(new Vector3D(0,    yMax, 0),   Vector3D.PLUS_J);<a name="line.115"></a>
<FONT color="green">116</FONT>            final Plane pzMin = new Plane(new Vector3D(0,    0,   zMin), Vector3D.MINUS_K);<a name="line.116"></a>
<FONT color="green">117</FONT>            final Plane pzMax = new Plane(new Vector3D(0,    0,   zMax), Vector3D.PLUS_K);<a name="line.117"></a>
<FONT color="green">118</FONT>            @SuppressWarnings("unchecked")<a name="line.118"></a>
<FONT color="green">119</FONT>            final Region&lt;Euclidean3D&gt; boundary =<a name="line.119"></a>
<FONT color="green">120</FONT>            new RegionFactory&lt;Euclidean3D&gt;().buildConvex(pxMin, pxMax, pyMin, pyMax, pzMin, pzMax);<a name="line.120"></a>
<FONT color="green">121</FONT>            return boundary.getTree(false);<a name="line.121"></a>
<FONT color="green">122</FONT>        }<a name="line.122"></a>
<FONT color="green">123</FONT>    <a name="line.123"></a>
<FONT color="green">124</FONT>        /** {@inheritDoc} */<a name="line.124"></a>
<FONT color="green">125</FONT>        @Override<a name="line.125"></a>
<FONT color="green">126</FONT>        public PolyhedronsSet buildNew(final BSPTree&lt;Euclidean3D&gt; tree) {<a name="line.126"></a>
<FONT color="green">127</FONT>            return new PolyhedronsSet(tree);<a name="line.127"></a>
<FONT color="green">128</FONT>        }<a name="line.128"></a>
<FONT color="green">129</FONT>    <a name="line.129"></a>
<FONT color="green">130</FONT>        /** {@inheritDoc} */<a name="line.130"></a>
<FONT color="green">131</FONT>        @Override<a name="line.131"></a>
<FONT color="green">132</FONT>        protected void computeGeometricalProperties() {<a name="line.132"></a>
<FONT color="green">133</FONT>    <a name="line.133"></a>
<FONT color="green">134</FONT>            // compute the contribution of all boundary facets<a name="line.134"></a>
<FONT color="green">135</FONT>            getTree(true).visit(new FacetsContributionVisitor());<a name="line.135"></a>
<FONT color="green">136</FONT>    <a name="line.136"></a>
<FONT color="green">137</FONT>            if (getSize() &lt; 0) {<a name="line.137"></a>
<FONT color="green">138</FONT>                // the polyhedrons set as a finite outside<a name="line.138"></a>
<FONT color="green">139</FONT>                // surrounded by an infinite inside<a name="line.139"></a>
<FONT color="green">140</FONT>                setSize(Double.POSITIVE_INFINITY);<a name="line.140"></a>
<FONT color="green">141</FONT>                setBarycenter(Vector3D.NaN);<a name="line.141"></a>
<FONT color="green">142</FONT>            } else {<a name="line.142"></a>
<FONT color="green">143</FONT>                // the polyhedrons set is finite, apply the remaining scaling factors<a name="line.143"></a>
<FONT color="green">144</FONT>                setSize(getSize() / 3.0);<a name="line.144"></a>
<FONT color="green">145</FONT>                setBarycenter(new Vector3D(1.0 / (4 * getSize()), (Vector3D) getBarycenter()));<a name="line.145"></a>
<FONT color="green">146</FONT>            }<a name="line.146"></a>
<FONT color="green">147</FONT>    <a name="line.147"></a>
<FONT color="green">148</FONT>        }<a name="line.148"></a>
<FONT color="green">149</FONT>    <a name="line.149"></a>
<FONT color="green">150</FONT>        /** Visitor computing geometrical properties. */<a name="line.150"></a>
<FONT color="green">151</FONT>        private class FacetsContributionVisitor implements BSPTreeVisitor&lt;Euclidean3D&gt; {<a name="line.151"></a>
<FONT color="green">152</FONT>    <a name="line.152"></a>
<FONT color="green">153</FONT>            /** Simple constructor. */<a name="line.153"></a>
<FONT color="green">154</FONT>            public FacetsContributionVisitor() {<a name="line.154"></a>
<FONT color="green">155</FONT>                setSize(0);<a name="line.155"></a>
<FONT color="green">156</FONT>                setBarycenter(new Vector3D(0, 0, 0));<a name="line.156"></a>
<FONT color="green">157</FONT>            }<a name="line.157"></a>
<FONT color="green">158</FONT>    <a name="line.158"></a>
<FONT color="green">159</FONT>            /** {@inheritDoc} */<a name="line.159"></a>
<FONT color="green">160</FONT>            public Order visitOrder(final BSPTree&lt;Euclidean3D&gt; node) {<a name="line.160"></a>
<FONT color="green">161</FONT>                return Order.MINUS_SUB_PLUS;<a name="line.161"></a>
<FONT color="green">162</FONT>            }<a name="line.162"></a>
<FONT color="green">163</FONT>    <a name="line.163"></a>
<FONT color="green">164</FONT>            /** {@inheritDoc} */<a name="line.164"></a>
<FONT color="green">165</FONT>            public void visitInternalNode(final BSPTree&lt;Euclidean3D&gt; node) {<a name="line.165"></a>
<FONT color="green">166</FONT>                @SuppressWarnings("unchecked")<a name="line.166"></a>
<FONT color="green">167</FONT>                final BoundaryAttribute&lt;Euclidean3D&gt; attribute =<a name="line.167"></a>
<FONT color="green">168</FONT>                    (BoundaryAttribute&lt;Euclidean3D&gt;) node.getAttribute();<a name="line.168"></a>
<FONT color="green">169</FONT>                if (attribute.getPlusOutside() != null) {<a name="line.169"></a>
<FONT color="green">170</FONT>                    addContribution(attribute.getPlusOutside(), false);<a name="line.170"></a>
<FONT color="green">171</FONT>                }<a name="line.171"></a>
<FONT color="green">172</FONT>                if (attribute.getPlusInside() != null) {<a name="line.172"></a>
<FONT color="green">173</FONT>                    addContribution(attribute.getPlusInside(), true);<a name="line.173"></a>
<FONT color="green">174</FONT>                }<a name="line.174"></a>
<FONT color="green">175</FONT>            }<a name="line.175"></a>
<FONT color="green">176</FONT>    <a name="line.176"></a>
<FONT color="green">177</FONT>            /** {@inheritDoc} */<a name="line.177"></a>
<FONT color="green">178</FONT>            public void visitLeafNode(final BSPTree&lt;Euclidean3D&gt; node) {<a name="line.178"></a>
<FONT color="green">179</FONT>            }<a name="line.179"></a>
<FONT color="green">180</FONT>    <a name="line.180"></a>
<FONT color="green">181</FONT>            /** Add he contribution of a boundary facet.<a name="line.181"></a>
<FONT color="green">182</FONT>             * @param facet boundary facet<a name="line.182"></a>
<FONT color="green">183</FONT>             * @param reversed if true, the facet has the inside on its plus side<a name="line.183"></a>
<FONT color="green">184</FONT>             */<a name="line.184"></a>
<FONT color="green">185</FONT>            private void addContribution(final SubHyperplane&lt;Euclidean3D&gt; facet, final boolean reversed) {<a name="line.185"></a>
<FONT color="green">186</FONT>    <a name="line.186"></a>
<FONT color="green">187</FONT>                final Region&lt;Euclidean2D&gt; polygon = ((SubPlane) facet).getRemainingRegion();<a name="line.187"></a>
<FONT color="green">188</FONT>                final double area    = polygon.getSize();<a name="line.188"></a>
<FONT color="green">189</FONT>    <a name="line.189"></a>
<FONT color="green">190</FONT>                if (Double.isInfinite(area)) {<a name="line.190"></a>
<FONT color="green">191</FONT>                    setSize(Double.POSITIVE_INFINITY);<a name="line.191"></a>
<FONT color="green">192</FONT>                    setBarycenter(Vector3D.NaN);<a name="line.192"></a>
<FONT color="green">193</FONT>                } else {<a name="line.193"></a>
<FONT color="green">194</FONT>    <a name="line.194"></a>
<FONT color="green">195</FONT>                    final Plane    plane  = (Plane) facet.getHyperplane();<a name="line.195"></a>
<FONT color="green">196</FONT>                    final Vector3D facetB = plane.toSpace(polygon.getBarycenter());<a name="line.196"></a>
<FONT color="green">197</FONT>                    double   scaled = area * facetB.dotProduct(plane.getNormal());<a name="line.197"></a>
<FONT color="green">198</FONT>                    if (reversed) {<a name="line.198"></a>
<FONT color="green">199</FONT>                        scaled = -scaled;<a name="line.199"></a>
<FONT color="green">200</FONT>                    }<a name="line.200"></a>
<FONT color="green">201</FONT>    <a name="line.201"></a>
<FONT color="green">202</FONT>                    setSize(getSize() + scaled);<a name="line.202"></a>
<FONT color="green">203</FONT>                    setBarycenter(new Vector3D(1.0, (Vector3D) getBarycenter(), scaled, facetB));<a name="line.203"></a>
<FONT color="green">204</FONT>    <a name="line.204"></a>
<FONT color="green">205</FONT>                }<a name="line.205"></a>
<FONT color="green">206</FONT>    <a name="line.206"></a>
<FONT color="green">207</FONT>            }<a name="line.207"></a>
<FONT color="green">208</FONT>    <a name="line.208"></a>
<FONT color="green">209</FONT>        }<a name="line.209"></a>
<FONT color="green">210</FONT>    <a name="line.210"></a>
<FONT color="green">211</FONT>        /** Get the first sub-hyperplane crossed by a semi-infinite line.<a name="line.211"></a>
<FONT color="green">212</FONT>         * @param point start point of the part of the line considered<a name="line.212"></a>
<FONT color="green">213</FONT>         * @param line line to consider (contains point)<a name="line.213"></a>
<FONT color="green">214</FONT>         * @return the first sub-hyperplaned crossed by the line after the<a name="line.214"></a>
<FONT color="green">215</FONT>         * given point, or null if the line does not intersect any<a name="line.215"></a>
<FONT color="green">216</FONT>         * sub-hyperplaned<a name="line.216"></a>
<FONT color="green">217</FONT>         */<a name="line.217"></a>
<FONT color="green">218</FONT>        public SubHyperplane&lt;Euclidean3D&gt; firstIntersection(final Vector3D point, final Line line) {<a name="line.218"></a>
<FONT color="green">219</FONT>            return recurseFirstIntersection(getTree(true), point, line);<a name="line.219"></a>
<FONT color="green">220</FONT>        }<a name="line.220"></a>
<FONT color="green">221</FONT>    <a name="line.221"></a>
<FONT color="green">222</FONT>        /** Get the first sub-hyperplane crossed by a semi-infinite line.<a name="line.222"></a>
<FONT color="green">223</FONT>         * @param node current node<a name="line.223"></a>
<FONT color="green">224</FONT>         * @param point start point of the part of the line considered<a name="line.224"></a>
<FONT color="green">225</FONT>         * @param line line to consider (contains point)<a name="line.225"></a>
<FONT color="green">226</FONT>         * @return the first sub-hyperplaned crossed by the line after the<a name="line.226"></a>
<FONT color="green">227</FONT>         * given point, or null if the line does not intersect any<a name="line.227"></a>
<FONT color="green">228</FONT>         * sub-hyperplaned<a name="line.228"></a>
<FONT color="green">229</FONT>         */<a name="line.229"></a>
<FONT color="green">230</FONT>        private SubHyperplane&lt;Euclidean3D&gt; recurseFirstIntersection(final BSPTree&lt;Euclidean3D&gt; node,<a name="line.230"></a>
<FONT color="green">231</FONT>                                                                    final Vector3D point,<a name="line.231"></a>
<FONT color="green">232</FONT>                                                                    final Line line) {<a name="line.232"></a>
<FONT color="green">233</FONT>    <a name="line.233"></a>
<FONT color="green">234</FONT>            final SubHyperplane&lt;Euclidean3D&gt; cut = node.getCut();<a name="line.234"></a>
<FONT color="green">235</FONT>            if (cut == null) {<a name="line.235"></a>
<FONT color="green">236</FONT>                return null;<a name="line.236"></a>
<FONT color="green">237</FONT>            }<a name="line.237"></a>
<FONT color="green">238</FONT>            final BSPTree&lt;Euclidean3D&gt; minus = node.getMinus();<a name="line.238"></a>
<FONT color="green">239</FONT>            final BSPTree&lt;Euclidean3D&gt; plus  = node.getPlus();<a name="line.239"></a>
<FONT color="green">240</FONT>            final Plane               plane = (Plane) cut.getHyperplane();<a name="line.240"></a>
<FONT color="green">241</FONT>    <a name="line.241"></a>
<FONT color="green">242</FONT>            // establish search order<a name="line.242"></a>
<FONT color="green">243</FONT>            final double offset = plane.getOffset(point);<a name="line.243"></a>
<FONT color="green">244</FONT>            final boolean in    = FastMath.abs(offset) &lt; 1.0e-10;<a name="line.244"></a>
<FONT color="green">245</FONT>            final BSPTree&lt;Euclidean3D&gt; near;<a name="line.245"></a>
<FONT color="green">246</FONT>            final BSPTree&lt;Euclidean3D&gt; far;<a name="line.246"></a>
<FONT color="green">247</FONT>            if (offset &lt; 0) {<a name="line.247"></a>
<FONT color="green">248</FONT>                near = minus;<a name="line.248"></a>
<FONT color="green">249</FONT>                far  = plus;<a name="line.249"></a>
<FONT color="green">250</FONT>            } else {<a name="line.250"></a>
<FONT color="green">251</FONT>                near = plus;<a name="line.251"></a>
<FONT color="green">252</FONT>                far  = minus;<a name="line.252"></a>
<FONT color="green">253</FONT>            }<a name="line.253"></a>
<FONT color="green">254</FONT>    <a name="line.254"></a>
<FONT color="green">255</FONT>            if (in) {<a name="line.255"></a>
<FONT color="green">256</FONT>                // search in the cut hyperplane<a name="line.256"></a>
<FONT color="green">257</FONT>                final SubHyperplane&lt;Euclidean3D&gt; facet = boundaryFacet(point, node);<a name="line.257"></a>
<FONT color="green">258</FONT>                if (facet != null) {<a name="line.258"></a>
<FONT color="green">259</FONT>                    return facet;<a name="line.259"></a>
<FONT color="green">260</FONT>                }<a name="line.260"></a>
<FONT color="green">261</FONT>            }<a name="line.261"></a>
<FONT color="green">262</FONT>    <a name="line.262"></a>
<FONT color="green">263</FONT>            // search in the near branch<a name="line.263"></a>
<FONT color="green">264</FONT>            final SubHyperplane&lt;Euclidean3D&gt; crossed = recurseFirstIntersection(near, point, line);<a name="line.264"></a>
<FONT color="green">265</FONT>            if (crossed != null) {<a name="line.265"></a>
<FONT color="green">266</FONT>                return crossed;<a name="line.266"></a>
<FONT color="green">267</FONT>            }<a name="line.267"></a>
<FONT color="green">268</FONT>    <a name="line.268"></a>
<FONT color="green">269</FONT>            if (!in) {<a name="line.269"></a>
<FONT color="green">270</FONT>                // search in the cut hyperplane<a name="line.270"></a>
<FONT color="green">271</FONT>                final Vector3D hit3D = plane.intersection(line);<a name="line.271"></a>
<FONT color="green">272</FONT>                if (hit3D != null) {<a name="line.272"></a>
<FONT color="green">273</FONT>                    final SubHyperplane&lt;Euclidean3D&gt; facet = boundaryFacet(hit3D, node);<a name="line.273"></a>
<FONT color="green">274</FONT>                    if (facet != null) {<a name="line.274"></a>
<FONT color="green">275</FONT>                        return facet;<a name="line.275"></a>
<FONT color="green">276</FONT>                    }<a name="line.276"></a>
<FONT color="green">277</FONT>                }<a name="line.277"></a>
<FONT color="green">278</FONT>            }<a name="line.278"></a>
<FONT color="green">279</FONT>    <a name="line.279"></a>
<FONT color="green">280</FONT>            // search in the far branch<a name="line.280"></a>
<FONT color="green">281</FONT>            return recurseFirstIntersection(far, point, line);<a name="line.281"></a>
<FONT color="green">282</FONT>    <a name="line.282"></a>
<FONT color="green">283</FONT>        }<a name="line.283"></a>
<FONT color="green">284</FONT>    <a name="line.284"></a>
<FONT color="green">285</FONT>        /** Check if a point belongs to the boundary part of a node.<a name="line.285"></a>
<FONT color="green">286</FONT>         * @param point point to check<a name="line.286"></a>
<FONT color="green">287</FONT>         * @param node node containing the boundary facet to check<a name="line.287"></a>
<FONT color="green">288</FONT>         * @return the boundary facet this points belongs to (or null if it<a name="line.288"></a>
<FONT color="green">289</FONT>         * does not belong to any boundary facet)<a name="line.289"></a>
<FONT color="green">290</FONT>         */<a name="line.290"></a>
<FONT color="green">291</FONT>        private SubHyperplane&lt;Euclidean3D&gt; boundaryFacet(final Vector3D point,<a name="line.291"></a>
<FONT color="green">292</FONT>                                                         final BSPTree&lt;Euclidean3D&gt; node) {<a name="line.292"></a>
<FONT color="green">293</FONT>            final Vector2D point2D = ((Plane) node.getCut().getHyperplane()).toSubSpace(point);<a name="line.293"></a>
<FONT color="green">294</FONT>            @SuppressWarnings("unchecked")<a name="line.294"></a>
<FONT color="green">295</FONT>            final BoundaryAttribute&lt;Euclidean3D&gt; attribute =<a name="line.295"></a>
<FONT color="green">296</FONT>                (BoundaryAttribute&lt;Euclidean3D&gt;) node.getAttribute();<a name="line.296"></a>
<FONT color="green">297</FONT>            if ((attribute.getPlusOutside() != null) &amp;&amp;<a name="line.297"></a>
<FONT color="green">298</FONT>                (((SubPlane) attribute.getPlusOutside()).getRemainingRegion().checkPoint(point2D) == Location.INSIDE)) {<a name="line.298"></a>
<FONT color="green">299</FONT>                return attribute.getPlusOutside();<a name="line.299"></a>
<FONT color="green">300</FONT>            }<a name="line.300"></a>
<FONT color="green">301</FONT>            if ((attribute.getPlusInside() != null) &amp;&amp;<a name="line.301"></a>
<FONT color="green">302</FONT>                (((SubPlane) attribute.getPlusInside()).getRemainingRegion().checkPoint(point2D) == Location.INSIDE)) {<a name="line.302"></a>
<FONT color="green">303</FONT>                return attribute.getPlusInside();<a name="line.303"></a>
<FONT color="green">304</FONT>            }<a name="line.304"></a>
<FONT color="green">305</FONT>            return null;<a name="line.305"></a>
<FONT color="green">306</FONT>        }<a name="line.306"></a>
<FONT color="green">307</FONT>    <a name="line.307"></a>
<FONT color="green">308</FONT>        /** Rotate the region around the specified point.<a name="line.308"></a>
<FONT color="green">309</FONT>         * &lt;p&gt;The instance is not modified, a new instance is created.&lt;/p&gt;<a name="line.309"></a>
<FONT color="green">310</FONT>         * @param center rotation center<a name="line.310"></a>
<FONT color="green">311</FONT>         * @param rotation vectorial rotation operator<a name="line.311"></a>
<FONT color="green">312</FONT>         * @return a new instance representing the rotated region<a name="line.312"></a>
<FONT color="green">313</FONT>         */<a name="line.313"></a>
<FONT color="green">314</FONT>        public PolyhedronsSet rotate(final Vector3D center, final Rotation rotation) {<a name="line.314"></a>
<FONT color="green">315</FONT>            return (PolyhedronsSet) applyTransform(new RotationTransform(center, rotation));<a name="line.315"></a>
<FONT color="green">316</FONT>        }<a name="line.316"></a>
<FONT color="green">317</FONT>    <a name="line.317"></a>
<FONT color="green">318</FONT>        /** 3D rotation as a Transform. */<a name="line.318"></a>
<FONT color="green">319</FONT>        private static class RotationTransform implements Transform&lt;Euclidean3D, Euclidean2D&gt; {<a name="line.319"></a>
<FONT color="green">320</FONT>    <a name="line.320"></a>
<FONT color="green">321</FONT>            /** Center point of the rotation. */<a name="line.321"></a>
<FONT color="green">322</FONT>            private Vector3D   center;<a name="line.322"></a>
<FONT color="green">323</FONT>    <a name="line.323"></a>
<FONT color="green">324</FONT>            /** Vectorial rotation. */<a name="line.324"></a>
<FONT color="green">325</FONT>            private Rotation   rotation;<a name="line.325"></a>
<FONT color="green">326</FONT>    <a name="line.326"></a>
<FONT color="green">327</FONT>            /** Cached original hyperplane. */<a name="line.327"></a>
<FONT color="green">328</FONT>            private Plane cachedOriginal;<a name="line.328"></a>
<FONT color="green">329</FONT>    <a name="line.329"></a>
<FONT color="green">330</FONT>            /** Cached 2D transform valid inside the cached original hyperplane. */<a name="line.330"></a>
<FONT color="green">331</FONT>            private Transform&lt;Euclidean2D, Euclidean1D&gt;  cachedTransform;<a name="line.331"></a>
<FONT color="green">332</FONT>    <a name="line.332"></a>
<FONT color="green">333</FONT>            /** Build a rotation transform.<a name="line.333"></a>
<FONT color="green">334</FONT>             * @param center center point of the rotation<a name="line.334"></a>
<FONT color="green">335</FONT>             * @param rotation vectorial rotation<a name="line.335"></a>
<FONT color="green">336</FONT>             */<a name="line.336"></a>
<FONT color="green">337</FONT>            public RotationTransform(final Vector3D center, final Rotation rotation) {<a name="line.337"></a>
<FONT color="green">338</FONT>                this.center   = center;<a name="line.338"></a>
<FONT color="green">339</FONT>                this.rotation = rotation;<a name="line.339"></a>
<FONT color="green">340</FONT>            }<a name="line.340"></a>
<FONT color="green">341</FONT>    <a name="line.341"></a>
<FONT color="green">342</FONT>            /** {@inheritDoc} */<a name="line.342"></a>
<FONT color="green">343</FONT>            public Vector3D apply(final Vector&lt;Euclidean3D&gt; point) {<a name="line.343"></a>
<FONT color="green">344</FONT>                final Vector3D delta = ((Vector3D) point).subtract(center);<a name="line.344"></a>
<FONT color="green">345</FONT>                return new Vector3D(1.0, center, 1.0, rotation.applyTo(delta));<a name="line.345"></a>
<FONT color="green">346</FONT>            }<a name="line.346"></a>
<FONT color="green">347</FONT>    <a name="line.347"></a>
<FONT color="green">348</FONT>            /** {@inheritDoc} */<a name="line.348"></a>
<FONT color="green">349</FONT>            public Plane apply(final Hyperplane&lt;Euclidean3D&gt; hyperplane) {<a name="line.349"></a>
<FONT color="green">350</FONT>                return ((Plane) hyperplane).rotate(center, rotation);<a name="line.350"></a>
<FONT color="green">351</FONT>            }<a name="line.351"></a>
<FONT color="green">352</FONT>    <a name="line.352"></a>
<FONT color="green">353</FONT>            /** {@inheritDoc} */<a name="line.353"></a>
<FONT color="green">354</FONT>            public SubHyperplane&lt;Euclidean2D&gt; apply(final SubHyperplane&lt;Euclidean2D&gt; sub,<a name="line.354"></a>
<FONT color="green">355</FONT>                                                    final Hyperplane&lt;Euclidean3D&gt; original,<a name="line.355"></a>
<FONT color="green">356</FONT>                                                    final Hyperplane&lt;Euclidean3D&gt; transformed) {<a name="line.356"></a>
<FONT color="green">357</FONT>                if (original != cachedOriginal) {<a name="line.357"></a>
<FONT color="green">358</FONT>                    // we have changed hyperplane, reset the in-hyperplane transform<a name="line.358"></a>
<FONT color="green">359</FONT>    <a name="line.359"></a>
<FONT color="green">360</FONT>                    final Plane    oPlane = (Plane) original;<a name="line.360"></a>
<FONT color="green">361</FONT>                    final Plane    tPlane = (Plane) transformed;<a name="line.361"></a>
<FONT color="green">362</FONT>                    final Vector3D p00    = oPlane.getOrigin();<a name="line.362"></a>
<FONT color="green">363</FONT>                    final Vector3D p10    = oPlane.toSpace(new Vector2D(1.0, 0.0));<a name="line.363"></a>
<FONT color="green">364</FONT>                    final Vector3D p01    = oPlane.toSpace(new Vector2D(0.0, 1.0));<a name="line.364"></a>
<FONT color="green">365</FONT>                    final Vector2D tP00   = tPlane.toSubSpace(apply(p00));<a name="line.365"></a>
<FONT color="green">366</FONT>                    final Vector2D tP10   = tPlane.toSubSpace(apply(p10));<a name="line.366"></a>
<FONT color="green">367</FONT>                    final Vector2D tP01   = tPlane.toSubSpace(apply(p01));<a name="line.367"></a>
<FONT color="green">368</FONT>                    final AffineTransform at =<a name="line.368"></a>
<FONT color="green">369</FONT>                        new AffineTransform(tP10.getX() - tP00.getX(), tP10.getY() - tP00.getY(),<a name="line.369"></a>
<FONT color="green">370</FONT>                                            tP01.getX() - tP00.getX(), tP01.getY() - tP00.getY(),<a name="line.370"></a>
<FONT color="green">371</FONT>                                            tP00.getX(), tP00.getY());<a name="line.371"></a>
<FONT color="green">372</FONT>    <a name="line.372"></a>
<FONT color="green">373</FONT>                    cachedOriginal  = (Plane) original;<a name="line.373"></a>
<FONT color="green">374</FONT>                    cachedTransform = org.apache.commons.math3.geometry.euclidean.twod.Line.getTransform(at);<a name="line.374"></a>
<FONT color="green">375</FONT>    <a name="line.375"></a>
<FONT color="green">376</FONT>                }<a name="line.376"></a>
<FONT color="green">377</FONT>                return ((SubLine) sub).applyTransform(cachedTransform);<a name="line.377"></a>
<FONT color="green">378</FONT>            }<a name="line.378"></a>
<FONT color="green">379</FONT>    <a name="line.379"></a>
<FONT color="green">380</FONT>        }<a name="line.380"></a>
<FONT color="green">381</FONT>    <a name="line.381"></a>
<FONT color="green">382</FONT>        /** Translate the region by the specified amount.<a name="line.382"></a>
<FONT color="green">383</FONT>         * &lt;p&gt;The instance is not modified, a new instance is created.&lt;/p&gt;<a name="line.383"></a>
<FONT color="green">384</FONT>         * @param translation translation to apply<a name="line.384"></a>
<FONT color="green">385</FONT>         * @return a new instance representing the translated region<a name="line.385"></a>
<FONT color="green">386</FONT>         */<a name="line.386"></a>
<FONT color="green">387</FONT>        public PolyhedronsSet translate(final Vector3D translation) {<a name="line.387"></a>
<FONT color="green">388</FONT>            return (PolyhedronsSet) applyTransform(new TranslationTransform(translation));<a name="line.388"></a>
<FONT color="green">389</FONT>        }<a name="line.389"></a>
<FONT color="green">390</FONT>    <a name="line.390"></a>
<FONT color="green">391</FONT>        /** 3D translation as a transform. */<a name="line.391"></a>
<FONT color="green">392</FONT>        private static class TranslationTransform implements Transform&lt;Euclidean3D, Euclidean2D&gt; {<a name="line.392"></a>
<FONT color="green">393</FONT>    <a name="line.393"></a>
<FONT color="green">394</FONT>            /** Translation vector. */<a name="line.394"></a>
<FONT color="green">395</FONT>            private Vector3D   translation;<a name="line.395"></a>
<FONT color="green">396</FONT>    <a name="line.396"></a>
<FONT color="green">397</FONT>            /** Cached original hyperplane. */<a name="line.397"></a>
<FONT color="green">398</FONT>            private Plane cachedOriginal;<a name="line.398"></a>
<FONT color="green">399</FONT>    <a name="line.399"></a>
<FONT color="green">400</FONT>            /** Cached 2D transform valid inside the cached original hyperplane. */<a name="line.400"></a>
<FONT color="green">401</FONT>            private Transform&lt;Euclidean2D, Euclidean1D&gt;  cachedTransform;<a name="line.401"></a>
<FONT color="green">402</FONT>    <a name="line.402"></a>
<FONT color="green">403</FONT>            /** Build a translation transform.<a name="line.403"></a>
<FONT color="green">404</FONT>             * @param translation translation vector<a name="line.404"></a>
<FONT color="green">405</FONT>             */<a name="line.405"></a>
<FONT color="green">406</FONT>            public TranslationTransform(final Vector3D translation) {<a name="line.406"></a>
<FONT color="green">407</FONT>                this.translation = translation;<a name="line.407"></a>
<FONT color="green">408</FONT>            }<a name="line.408"></a>
<FONT color="green">409</FONT>    <a name="line.409"></a>
<FONT color="green">410</FONT>            /** {@inheritDoc} */<a name="line.410"></a>
<FONT color="green">411</FONT>            public Vector3D apply(final Vector&lt;Euclidean3D&gt; point) {<a name="line.411"></a>
<FONT color="green">412</FONT>                return new Vector3D(1.0, (Vector3D) point, 1.0, translation);<a name="line.412"></a>
<FONT color="green">413</FONT>            }<a name="line.413"></a>
<FONT color="green">414</FONT>    <a name="line.414"></a>
<FONT color="green">415</FONT>            /** {@inheritDoc} */<a name="line.415"></a>
<FONT color="green">416</FONT>            public Plane apply(final Hyperplane&lt;Euclidean3D&gt; hyperplane) {<a name="line.416"></a>
<FONT color="green">417</FONT>                return ((Plane) hyperplane).translate(translation);<a name="line.417"></a>
<FONT color="green">418</FONT>            }<a name="line.418"></a>
<FONT color="green">419</FONT>    <a name="line.419"></a>
<FONT color="green">420</FONT>            /** {@inheritDoc} */<a name="line.420"></a>
<FONT color="green">421</FONT>            public SubHyperplane&lt;Euclidean2D&gt; apply(final SubHyperplane&lt;Euclidean2D&gt; sub,<a name="line.421"></a>
<FONT color="green">422</FONT>                                                    final Hyperplane&lt;Euclidean3D&gt; original,<a name="line.422"></a>
<FONT color="green">423</FONT>                                                    final Hyperplane&lt;Euclidean3D&gt; transformed) {<a name="line.423"></a>
<FONT color="green">424</FONT>                if (original != cachedOriginal) {<a name="line.424"></a>
<FONT color="green">425</FONT>                    // we have changed hyperplane, reset the in-hyperplane transform<a name="line.425"></a>
<FONT color="green">426</FONT>    <a name="line.426"></a>
<FONT color="green">427</FONT>                    final Plane   oPlane = (Plane) original;<a name="line.427"></a>
<FONT color="green">428</FONT>                    final Plane   tPlane = (Plane) transformed;<a name="line.428"></a>
<FONT color="green">429</FONT>                    final Vector2D shift  = tPlane.toSubSpace(apply(oPlane.getOrigin()));<a name="line.429"></a>
<FONT color="green">430</FONT>                    final AffineTransform at =<a name="line.430"></a>
<FONT color="green">431</FONT>                        AffineTransform.getTranslateInstance(shift.getX(), shift.getY());<a name="line.431"></a>
<FONT color="green">432</FONT>    <a name="line.432"></a>
<FONT color="green">433</FONT>                    cachedOriginal  = (Plane) original;<a name="line.433"></a>
<FONT color="green">434</FONT>                    cachedTransform =<a name="line.434"></a>
<FONT color="green">435</FONT>                            org.apache.commons.math3.geometry.euclidean.twod.Line.getTransform(at);<a name="line.435"></a>
<FONT color="green">436</FONT>    <a name="line.436"></a>
<FONT color="green">437</FONT>                }<a name="line.437"></a>
<FONT color="green">438</FONT>    <a name="line.438"></a>
<FONT color="green">439</FONT>                return ((SubLine) sub).applyTransform(cachedTransform);<a name="line.439"></a>
<FONT color="green">440</FONT>    <a name="line.440"></a>
<FONT color="green">441</FONT>            }<a name="line.441"></a>
<FONT color="green">442</FONT>    <a name="line.442"></a>
<FONT color="green">443</FONT>        }<a name="line.443"></a>
<FONT color="green">444</FONT>    <a name="line.444"></a>
<FONT color="green">445</FONT>    }<a name="line.445"></a>




























































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